Geometry - Polygons

In geometry a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

The word "polygon" derives from the Greek πολύς ("many") and γωνία (gōnia), meaning "knee" or "angle". Today a polygon is more usually understood in terms of sides. - Wikipedia

    K = area
    r= radius of inscribed circle
    R = radius of circumscribed circle
    p and q are diagonals
    n= number of sides
    θ = one of the vertex angles

Right Triangle  (Pythagorean)

Equilateral Triangle

Rectangle

Parallelogram

General Quadrilateral       (Bretschneider's Formula)

Cyclic-Inscriptable Quadrilateral

General Triangle hc = length of altitude on side c, tc = length of bisector of angle C, mc = length of median to side c. (Law of Cosines) (Heron’s formula)

Rhombus

Trapezoid

Regular Polygon

Cyclic Quadrilateral    (Brahmagupta’s formula)

Source: CRC Standard Math Tables, 1987